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Linear programming problems are optimization problems where the objective function and constraints are all linear. Mathematica has a collection of algorithms for solving linear optimization problems with real variables, accessed via LinearProgramming, FindMinimum, FindMaximum, NMinimize, NMaximize, Minimize, and Maximize. LinearProgramming gives direct access to linear program- ming algorithms, provides the most flexibility for specifying the methods used, and is the most efficient for large-scale problems. FindMi...

Constrained optimization problems are problems for which a function f (x) is to be minimized or maximized subject to constraints ? (x) . Here f : Rn ? R is called the objective function and F(x) is a Boolean-valued formula. In Mathematica the constraints ? (x) can be an arbitrary Boolean combination of equations g (x) ?0 , weak inequalities g (x) >=0, strict inequalities g(x)> 0, x is integer and x>0 statements. A point u ? Rn is said to be a global minimum of f subject to constraints F if u satisfies the constrai...